Heterodyne polarization interference imaging spectroscopy

Abstract

A novel heterodyne polarization interference imaging spectroscopy (HPⅡS) based on a Savart polariscope is proposed in this paper. The HPⅡS is modified by introducing a pair of parallel polarization gratings into the static polarization interference imaging spectrometer. Because of the introduced parallel polarization gratings, the lateral displacements of the two beams split by the Savart polariscope vary with wavenumber. The frequency of the interferogram obtained on the detector is related to wavenumber. Like the spatial heterodyne spectrometer where the two end mirrors in a Michelson interferometer are replaced with two matched diffraction gratings, the zero frequency of the interferogram generated in HPⅡS corresponds to a heterodyne wavenumber instead of the zero wavenumber in a non-heterodyne spectrometer. Due to the heterodyne characteristics, a high spectral resolution can be achieved using a small number of sampling points. In addition, there is no slit in HPⅡS and it is an imaging Fourier transform spectrometer that records a two-dimensional image of a scene superimposed with interference curves. It is a temporally and spatially combined modulated Fourier transform spectrometer and the interferogram of one point from the scene is generated by picking up the corresponding pixels from a sequence of images which are acquired by scanning the scene. As a true imaging spectrometer, HPⅡS also has high sensitivity and high signal-to-noise ratio. In this paper, the basic principle of HPⅡS is studied. The optical path difference produced by the Savart polariscope and the parallel polarization gratings is calculated. The interferogram expression, the spectral resolution, and the spectrum reconstruction method are elaborated. As the relationship between the frequency of the interferogram and the wavenumber of the incident light is nonlinear, the input spectrum can be recovered using Fourier transform combined with the method of stationary phase. Also, the matrix inversion method can be used to recover the input spectrum. Finally, a design example of HPⅡS is given. The interferogram is simulated, and the recovered spectrum shows good agreement with the input spectrum. In the design example, the spectral range is 16667-18182 cm-1(550-600 nm), and the number of sampling points is 500. The spectral resolution of HPⅡS is 6.06 cm-1, which is 12 times smaller than that in a non-heterodyne spectrometer with the same spectral range and sampling numbers. HPⅡS has the advantages of compact structure, high optical throughput, strong stability, and high spectral resolution. It is especially suitable for hyperspectral detection with ultra-small, high stability, and high sensitivity.